skip to main content


Title: A data-driven method for estimating the composition of end-members from stream water chemistry time series
Abstract. End-member mixing analysis (EMMA) is a method of interpreting stream water chemistry variations and is widely used for chemical hydrograph separation. It is based on the assumption that stream water is a conservative mixture of varying contributions from well-characterized source solutions (end-members). These end-members are typically identified by collecting samples of potential end-member source waters from within the watershed and comparing these to the observations. Here we introduce a complementary data-driven method (convex hull end-member mixing analysis – CHEMMA) to infer the end-member compositions and their associated uncertainties from the stream water observations alone. The method involves two steps. The first uses convex hull nonnegative matrix factorization (CH-NMF) to infer possible end-member compositions by searching for a simplex that optimally encloses the stream water observations. The second step uses constrained K-means clustering (COP-KMEANS) to classify the results from repeated applications of CH-NMF and analyzes the uncertainty associated with the algorithm. In an example application utilizing the 1986 to 1988 Panola Mountain Research Watershed dataset, CHEMMA is able to robustly reproduce the three field-measured end-members found in previous research using only the stream water chemical observations. CHEMMA also suggests that a fourth and a fifth end-member can be (less robustly) identified. We examine uncertainties in end-member identification arising from non-uniqueness, which is related to the data structure, of the CH-NMF solutions, and from the number of samples using both real and synthetic data. The results suggest that the mixing space can be identified robustly when the dataset includes samples that contain extremely small contributions of one end-member, i.e., samples containing extremely large contributions from one end-member are not necessary but do reduce uncertainty about the end-member composition.  more » « less
Award ID(s):
1654194
NSF-PAR ID:
10336617
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Hydrology and Earth System Sciences
Volume:
26
Issue:
8
ISSN:
1607-7938
Page Range / eLocation ID:
1977 to 1991
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Stable isotope variations are extremely useful for flow partitioning within the hydrologic cycle but remain poorly understood throughout the tropics, particularly in watersheds with rapidly infiltrating soils, such as Andisols in Central America. This study examines the fluctuations of stable isotope ratios (δ18O and δ2H) in the hydrologic components of a tropical coffee agroforestry watershed (~1 km2) with Andisol soils in Costa Rica. Samples were collected in precipitation, groundwater, springs, and stream water over 2 years. The local meteoric water line for the study site was δ2H = 8.5 δ18O + 18.02 (r2 = 0.97,n = 198). The isotope ratios in precipitation exhibited an enriched trend during the dry season and a notable depletion at the beginning of the wet season. The δ18O compositions in groundwater (average = −6.4‰, σ = 0.7) and stream water (average = −6.7‰, σ = 0.6) were relatively stable over time, and both components exhibited more enriched values in 2013, which was the drier year. No strong correlation was observed between the isotope ratios and the precipitation amount at the event or daily time‐step, but a correlation was observed on a monthly scale. Stream water and base flow hydrograph separations based on isotope end‐member estimations showed that pre‐event water originating from base flow was prevalent. However, isotope data indicate that event water originating from springs appears to have been the primary driver of initial rises in stream flow and peak flows. These results indicate that isotope sampling improves the understanding of water balance components, even in a tropical humid location, where significant variations in rainfall challenge current modelling efforts. Further research using fine‐scale hydrometric and isotopic data would enhance understanding the processes driving spring flow generation in watersheds.

     
    more » « less
  2. Active learning is a valuable tool for efficiently exploring complex spaces, finding a variety of uses in materials science. However, the determination of convex hulls for phase diagrams does not neatly fit into traditional active learning approaches due to their global nature. Specifically, the thermodynamic stability of a material is not simply a function of its own energy, but rather requires energetic information from all other competing compositions and phases. Here we present Convex hull-aware Active Learning (CAL), a novel Bayesian algorithm that chooses experiments to minimize the uncertainty in the convex hull. CAL prioritizes compositions that are close to or on the hull, leaving significant uncertainty in other compositions that are quickly determined to be irrelevant to the convex hull. The convex hull can thus be predicted with significantly fewer observations than approaches that focus solely on energy. Intrinsic to this Bayesian approach is uncertainty quantification in both the convex hull and all subsequent predictions (e.g., stability and chemical potential). By providing increased search efficiency and uncertainty quantification, CAL can be readily incorporated into the emerging paradigm of uncertainty-based workflows for thermodynamic prediction. 
    more » « less
  3. Abstract

    The shallow and deep hypothesis suggests that stream concentration‐discharge (CQ) relationships are shaped by distinct source waters from different depths. Under this hypothesis, baseflows are typically dominated by groundwater and mostly reflect groundwater chemistry, whereas high flows are typically dominated by shallow soil water and mostly reflect soil water chemistry. Aspects of this hypothesis draw on applications like end member mixing analyses and hydrograph separation, yet direct data support for the hypothesis remains scarce. This work tests the shallow and deep hypothesis using co‐located measurements of soil water, groundwater, and streamwater chemistry at two intensively monitored sites, the W‐9 catchment at Sleepers River (Vermont, United States) and the Hafren catchment at Plynlimon (Wales). At both sites, depth profiles of subsurface water chemistry and stream CQ relationships for the 10 solutes analyzed are broadly consistent with the hypothesis. Solutes that are more abundant at depth (e.g., calcium) exhibit dilution patterns (concentration decreases with increasing discharge). Conversely, solutes enriched in shallow soils (e.g., nitrate) generally exhibit flushing patterns (concentration increases with increasing discharge). The hypothesis may hold broadly true for catchments that share such biogeochemical stratifications in the subsurface. Soil water and groundwater chemistries were estimated from high‐ and low‐flow stream chemistries with average relative errors ranging from 24% to 82%. This indicates that streams mirror subsurface waters: stream chemistry can be used to infer scarcely measured subsurface water chemistry, especially where there are distinct shallow and deep end members.

     
    more » « less
  4. Abstract

    Observations from a granitic watershed within a Mediterranean climate reveal the hydrologic and critical zone functioning of a perennial stream headwater and its upslope contributing area within a meadow system in the Sierra Nevada, California. Chemical analysis (diagnostic tools of mixing models, end member mixing analysis, tritium, etc.) and physical data (stream stage, piezometers, soil water, snowpack, etc.) indicate there are two primary pathways of water input into a headwater stream sourced from a mountain meadow. One input is a shallower and younger subsurface pathway with water that resembles snowpack chemistry, and the other a deeper and older subsurface pathway with water that reflects the chemistry of the groundwater derived from the contributing hillslopes. Multi‐year observations reveal that regardless of snowpack amount, during the period of peak hillslope infiltration, shallow and deep pathways in the hillslope behave similarly to initiate headwater streams. However, during summer dry periods, similarities in active pathways within the meadow center are not maintained between high and low snowpack years. With less snow, perennial groundwater discharge within the meadow center is eliminated, becoming only a seasonal source at the meadow's outlet. At the meadow's edge, geophysically observed downslope thinning in saprolite thickness creates reduced lateral transmissivity and initiation points for headwater streams via enhanced groundwater discharge of upslope water. Combined, these findings suggest how loss of snowpack and critical zone structure can together mediate hydrologic function in a wet meadow system in a Mediterranean climate. Creating new understanding about the stability of hydraulic functioning in headwater wet‐meadow systems under a changing climate.

     
    more » « less
  5. Abstract

    In snowmelt‐driven mountain watersheds, the hydrologic connectivity between meteoric waters and stream flow generation varies strongly with the season, reflecting variable connection to soil and groundwater storage within the watershed. This variable connectivity regulates how streamflow generation mechanisms transform the seasonal and elevational variation in oxygen and hydrogen isotopic composition (δ18O and δD) of meteoric precipitation. Thus, water isotopes in stream flow can signal immediate connectivity or more prolonged mixing, especially in high‐relief mountainous catchments. We characterized δ18O and δD values in stream water along an elevational gradient in a mountain headwater catchment in southwestern Montana. Stream water isotopic compositions related most strongly to elevation between February and March, exhibiting higher δ18O and δD values with decreasing elevation. These elevational isotopic lapse rates likely reflect increased connection between stream flow and proximal snow‐derived water sources heavily subject to elevational isotopic effects. These patterns disappeared during summer sampling, when consistently lower δ18O and δD values of stream water reflected contributions from snowmelt or colder rainfall, despite much higher δ18O and δD values expected in warmer seasonal rainfall. The consistently low isotopic values and absence of a trend with elevation during summer suggest lower connectivity between summer precipitation and stream flow generation as a consequence of drier soils and greater transpiration. As further evidence of intermittent seasonal connectivity between the stream and adjacent groundwaters, we observed a late‐winter flush of nitrate into the stream at higher elevations, consistent with increased connection to accumulating mineralized nitrogen in riparian wetlands. This pattern was distinct from mid‐summer patterns of nitrate loading at lower elevations that suggested heightened human recreational activity along the stream corridor. These observations provide insights linking stream flow generation and seasonal water storage in high elevation mountainous watersheds. Greater understanding of the connections between surface water, soil water and groundwater in these environments will help predict how the quality and quantity of mountain runoff will respond to changing climate and allow better informed water management decisions.

     
    more » « less